One-third of American workers aren’t sleeping enough to function at peak levels, and that chronic exhaustion is costing billions of dollars in lost productivity, according to researchers from Harvard Medical School.

Managers at a growing number of concerns, among them Procter & Gamble and Goldman Sachs, are waking up to the problem, investing in programs from sleep-hygiene courses to melatonin-regulating lighting to help employees improve their slumber.

The Centers for Disease Control and Prevention estimates 40.6 million American workers, or 30 percent of the civilian workforce, don’t get enough rest. And the Harvard scientists estimated in 2011 that sleep deprivation costs U.S. companies $63.2 billion in lost productivity per year, mainly because of “presenteeism,” people showing up for work but operating at subpar levels. One example, from a separate team at Singapore Management University: Workers waste an extra 8.4 minutes online — checking email, refreshing the TMZ.com home page, and so on — for every hour of interrupted sleep the previous night.

Managers struggle to motivate exhausted workers. During busy holiday periods at the Park Hyatt Beaver Creek resort in Avon, Colo., long hours sometimes lead to short fuses among staff. “You have to try to figure out who’s feeling frustrated and help them cut loose to get some rest,” said Scott Gubrud, director of sales and marketing at the hotel, which last week began a series of better-sleep initiatives for both employees and guests.

“If we treated machinery like we treat the human body, there would be breakdowns all the time,” said James Maas, a former Cornell University psychologist and author of “Sleep for Success.”

Companies have been slow to grasp the effects of sleep deprivation on productivity, but it is now a hot topic even in hard-driving industries, such as finance, where pulling all-nighters is often viewed as crucial to getting ahead.

Maas, who says he coined the phrase “power nap” 36 years ago, gave a talk about sleep hygiene at Goldman Sachs in 2011 that was so oversubscribed it had to be broadcast via conference call to accommodate the 1,000 or so people who wanted to attend. He spoke last year at hedge-fund firm D.E. Shaw & Co., which has nap pods scattered around its offices.

Yet perceptions linger that sleep is for sissies and loafers, and neither Goldman nor Shaw would comment directly about why they’re addressing employees’ sleep habits. A 2012 University of Southern California study of young investment bankers suggests that punishing hours, and resulting sleep deprivation, contributed to physical and emotional ailments within four years on the job.

“People in investment banking have been my main clients for the last few years because they’re so exhausted and under so much pressure,” said Maas, adding that bankers usually don’t want to hear about how to get more sleep. Instead, they want tips for performing well on five or six hours’ rest.

The risks of fatigue are especially acute in professions like health care and manufacturing, which involve overnight shifts and where a single careless error can put lives in danger.

At Aurora Health Care, the largest hospital system in Wisconsin, more than 2,600 employees in 2012 took a six-week online course for insomnia sufferers after managers surmised that sleep deprivation was likely a problem among its workforce. The course, one of several health-coaching sessions offered at Aurora and developed by Johnson & Johnson’s Wellness & Prevention unit, requires participants to keep a sleep diary, and then makes recommendations based on individual sleep patterns.

Barb Stollenwork, age 53 and a wellness program coordinator at Aurora, kicked her nightly Tylenol PM habit after finishing the program at the end of 2011. For years, she said, she woke at 4 a.m., then lay in bed worrying about how she’d function that day. By changing her behavior — for instance, going to bed later — she began sleeping until her alarm rang at 5:30 a.m.

Based on follow-up surveys that asked about both sleep and work habits, Aurora sees an average of $672 in productivity savings per participant in the insomnia module, said Dr. David Smith, an Aurora vice president.

Procter & Gamble is talking with sleep expert Nancy Rothstein about creating a multiweek pilot program for two of its plants, one in Belleville, Ontario, that makes Always feminine-hygiene products, and the other in Lima, Ohio, that makes liquid laundry detergents. Paul DeLuca, North American learning and development manager, said he hopes to have both courses running by June, starting with a group of 15 to 20 workers in Lima and up to 300 in Belleville.

The plants operate day and night, so many employees work unconventional hours, a known risk for poor sleep and overall bad health. If the program helps workers get better rest, with resulting gains in productivity and concentration, DeLuca will argue for a broader rollout of the initiative.

P&G brought Rothstein to its headquarters in Cincinnati last year to give a 50-minute presentation emphasizing, among other things, the importance of shutting off screen devices an hour before bed because the blue light emitted by the screens interferes with production of the sleep hormone melatonin.

That’s no easy order in the age of smartphones, laptops and late-night conference calls with the Beijing or London office. “The line between work and what’s outside of work is graying,” DeLuca said.

At the more extreme end of the intervention scale, some are calling upon Litebook Company Ltd., a Canadian maker of lights that help regulate the body’s melatonin levels. The company, which supplies devices to the Philadelphia Flyers and Ottawa Senators to help athletes cope with jet lag and game schedules, said it is getting calls from corporations interested in making the lights available at workstations and desks.

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